# <span lang="EN-US

Given: BD = DC and DL AB and DM AC such that DL=DM

To prove: AB = AC

Proof:

In right angled triangles ∆BLD and ∆CMD,

BLD = CMD = 90°

BD = CD … given

DL = DM … given

Thus by right angled hypotenuse side property of congruence,

∆BLD CMD

Hence, we know that, corresponding parts of the congruent triangles are equal

ABD = ACD

In ∆ABC, we have,

ABD = ACD

AB= AC …. Sides opposite to equal angles are equal

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